TRANSFORMATIONS AND OUTLIERS
Critical examination of the data is an important step in statistical analyses. Often, we observe either what seem to be unusual observations (outliers) or observations that appear to violate the assumptions of the analysis. When such problems occur, several courses of action are available depending on the nature of the problem and statistical judgement. Most of the analyses described in previous chapters are appropriate for groups in which data are normally distributed with equal variance. As a result of the Central Limit theorem, these analyses perform well for data that are not normal provided the deviation from normality is not large and/or the data sets are not very small. (If necessary and appropriate, nonparametric analyses, Chap. 15, can be used in these instances.) However, lack of equality of variance (heteroscedascity) in t tests, analysis of variance and regression, for example, is more problematic. The Fisher-Behrens test is an example of a modified analysis that is used in the comparison of means from two independent groups with unequal variances in the two groups (Chapter 5). Often, variance heterogeneity and/or lack of normality can be corrected by a data transformation, such as the logarithmic or square root transformation. Bioequivalence parameters such as AUC and CMAX currently require a log transformation prior to statistical analysis. Transformations of data may also be appropriate to help linearize data. For example, a plot of log potency vs. time is linear for stability data showing first-order kinetics.